{
  "id": "1806.07502",
  "version": "v1",
  "published": "2018-06-19T23:33:45.000Z",
  "updated": "2018-06-19T23:33:45.000Z",
  "title": "Time-dependent polynomials with one double root, and related new solvable systems of nonlinear evolution equations",
  "authors": [
    "Oksana Bihun",
    "Francesco Calogero"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Recently new solvable systems of nonlinear evolution equations -- including ODEs, PDEs and systems with discrete time -- have been introduced. These findings are based on certain convenient formulas expressing the $k$-th time-derivative of a root of a time-dependent monic polynomial in terms of the $k$-th time-derivative of the coefficients of the same polynomial and of the roots of the same polynomial as well as their time-derivatives of order less than $k$. These findings were restricted to the case of generic polynomials without any multiple root. In this paper some of these findings -- those for $k=1$ and $k=2$ -- are extended to polynomials featuring one double root; and a few representative examples are reported of new solvable systems of nonlinear evolution equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-19T23:33:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10",
      "70K42"
    ],
    "keywords": [
      "nonlinear evolution equations",
      "solvable systems",
      "double root",
      "time-dependent polynomials",
      "time-dependent monic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}